% !TeX root =main.tex
\begin{table}[h]
	\caption{Number of trees per species in dataset \#1; measured ranges of tree diameter ($DBH$), height and total volume ($Vtot$). Species common to dataset \#1 and \#2 are highlighted in gray.}
	\bigskip
	\centering
	\small
		\begin{tabular}{llccccc}
			\hline
			Genus & Species & Number & $DBH$ range	& $Height$ range	& $Vtot$ range \\
			           &               & of trees & (cm)		& (m)		& (m$^3$) \\
			\hline
		% début auto
			\multicolumn{6}{c}{Angiosperms}\\
			\rowcolor[gray]{0.9}
			\textit{Betula} & \textit{pendula} & 16 & $ 12- 31$ & $14.7 - 28.5$ & $0.08 - 1.02$ \\
			\rowcolor[gray]{0.9}
			\textit{Carpinus} & \textit{betulus} & 77 & $  8- 38$ & $11.3 - 30.0$ & $0.03 - 2.38$ \\
			\rowcolor[gray]{0.9}
			\textit{Fagus} & \textit{sylvatica} & 1987 & $  7- 79$ & $ 5.5 - 42.5$ & $0.01 - 7.46$ \\
			\rowcolor[gray]{0.9}
			\textit{Fraxinus} & \textit{excelsior} & 115 & $  8- 43$ & $11.5 - 26.7$ & $0.04 - 2.47$ \\
			\textit{Quercus} & \textit{palustris} & 24 & $  7- 24$ & $ 8.9 - 16.5$ & $0.02 - 0.44$ \\
			\rowcolor[gray]{0.9}
			\textit{Quercus} & \textit{petraea/robur} & 1748 & $  7-102$ & $ 6.0 - 40.0$ & $0.02 - 18.12$ \\
			\textit{Quercus} & \textit{rubra} & 110 & $  7- 35$ & $10.9 - 23.5$ & $0.03 - 0.96$ \\
			\hline
			\multicolumn{6}{c}{Gymnosperms}\\
			\textit{Abies} & \textit{alba} & 1095 & $  7- 90$ & $ 6.9 - 37.8$ & $0.02 - 10.25$ \\
			\textit{Abies} & \textit{nordmanniana} & 40 & $  7- 38$ & $ 3.5 - 27.0$ & $0.02 - 1.62$ \\
			\textit{Larix} & \textit{decidua} & 92 & $  9- 42$ & $ 9.0 - 25.6$ & $0.04 - 1.95$ \\
			\textit{Picea} & \textit{abies} & 318 & $  8- 67$ & $ 7.7 - 41.3$ & $0.02 - 6.59$ \\
			\textit{Picea} & \textit{sitchensis} & 12 & $  9- 14$ & $ 9.5 - 14.0$ & $0.04 - 0.14$ \\
			\textit{Pinus} & \textit{laricio} & 158 & $ 13- 51$ & $13.3 - 33.4$ & $0.08 - 3.68$ \\
			\textit{Pinus} & \textit{nigra} & 23 & $ 10- 35$ & $ 8.9 - 27.0$ & $0.04 - 1.28$ \\
			\textit{Pinus} & \textit{pinaster} & 777 & $  7- 44$ & $ 5.1 - 23.5$ & $0.01 - 1.70$ \\
			\textit{Pinus} & \textit{strobus} & 32 & $  8- 36$ & $ 7.9 - 25.0$ & $0.03 - 1.34$ \\
			\textit{Pinus} & \textit{sylvestris} & 1012 & $  7- 71$ & $ 9.4 - 29.3$ & $0.02 - 7.70$ \\
			\textit{Pinus} & \textit{uncinata} & 166 & $  8- 40$ & $ 6.7 - 20.5$ & $0.03 - 1.65$ \\
			\textit{Pseudotsuga} & \textit{menziesii} & 390 & $  7- 34$ & $ 7.0 - 29.5$ & $0.02 - 1.12$ \\
			\hline
			Total & 19 species & 8192 & $  7-102$ & $ 3.5 - 42.5$ & $0.01 - 18.12$ \\
			\hline
		% fin auto

		\end{tabular}
	\label{tableEssences1}
\end{table}

\begin{table}[h]
	\caption{Number of trees per species in dataset \#2; measured ranges of tree diameter ($DBH$), height and total volume ($Vtot$). Species common to dataset \#1 and \#2 are highlighted in gray.}
	\bigskip
	\centering
	\small
		\begin{tabular}{llccccc}
			\hline
			Genus & Species & Number & $DBH$ range	& $Height$ range	& $Vtot$ range \\
			           &               & of trees & (cm)		& (m)		& (m$^3$) \\
			\hline
		% début auto
			\multicolumn{6}{c}{Angiosperms}\\
			\textit{Acer} & \textit{pseudoplatanus} & 23 & $ 12- 43$ & $16.3 - 22.9$ & $0.10 - 2.15$ \\
			\rowcolor[gray]{0.9}
			\textit{Betula} & \textit{pendula} & 13 & $ 10- 52$ & $10.1 - 28.9$ & $0.04 - 3.94$ \\
			\rowcolor[gray]{0.9}
			\textit{Carpinus} & \textit{betulus} & 2 & $ 19- 30$ & $18.2 - 22.9$ & $0.30 - 1.04$ \\
			\rowcolor[gray]{0.9}
			\textit{Fagus} & \textit{sylvatica} & 34 & $ 11- 76$ & $16.8 - 27.1$ & $0.08 - 10.72$ \\
     			\rowcolor[gray]{0.9}
			\textit{Fraxinus} & \textit{excelsior} & 8 & $ 26- 65$ & $20.6 - 29.9$ & $0.74 - 7.36$ \\
			\textit{Populus} & \textit{tremula} & 2 & $ 22- 30$ & $21.8 - 25.9$ & $0.58 - 0.95$ \\
			\textit{Quercus} & \textit{ilex} & 23 & $  7- 20$ & $ 4.2 - 10.4$ & $0.01 - 0.22$ \\
			\rowcolor[gray]{0.9}
			\textit{Quercus} & \textit{petraea/robur} & 24 & $ 18- 94$ & $16.2 - 32.8$ & $0.20 - 13.04$ \\
			\textit{Quercus} & \textit{pubescens} & 8 & $ 22- 46$ & $16.5 - 20.4$ & $0.46 - 2.01$ \\
			\textit{Alnus} & \textit{sp.} & 16 & $ 24- 49$ & $17.7 - 28.0$ & $0.57 - 2.95$ \\
			\textit{Robinia} & \textit{pseudoacacia} & 8 & $ 15- 24$ & $20.1 - 23.5$ & $0.19 - 0.55$ \\
			\textit{Tilia} & \textit{sp.} & 7 & $ 21- 43$ & $22.9 - 25.1$ & $0.54 - 2.89$ \\
			\hline
			\multicolumn{6}{c}{Gymnosperms}\\
			\textit{Pinus} & \textit{halepensis} & 8 & $ 18- 64$ & $10.9 - 17.7$ & $0.17 - 3.52$ \\
			\hline
			Total & 13 species & 176 & $  7- 94$ & $ 4.2 - 32.8$ & $0.01 - 13.04$ \\
			\hline
		% fin auto

		\end{tabular}
	\label{tableEssences2}
\end{table}

\bigskip


\begin{table}[h]
	\caption{RMSE and relative RMSE (in brackets) for $VEF$ and $Vtot$ computed by diameter classes (model corresponding to Equation \eqref{equa7} fitted on the whole calibration dataset \#1).}
	\bigskip
	\centering 
	\scriptsize
		\begin{tabular}{lccccc}
			\hline
			$DBH$ (cm) & [7-10[ & $\left[10-20\right[$ & $\left[20-30\right[$ & $\left[30-40\right[$ & $\geq40$ \\
			\hline			
			n & 893 & 3308 & 2336 & 939 & 716 \\	
			RMSE of $VEF$ & 0.251 (16.2\%) & 0.095 (8.0\%) & 0.102 (8.8\%) & 0.136 (11.5\%) & 0.180 (14.3\%) \\
			RMSE of $Vtot$ (m$^{3}$) & 0.005 (12.9\%) & 0.014 (8.0\%) & 0.050 (8.7\%) & 0.142 (10.4\%) & 0.476 (13.7\%) \\ 
			\hline
		\end{tabular}
	\label{table_RMSE_vs_diameter_class}
\end{table}


\begin{table}[h]
	\caption{Parameter estimates by genus based on BLUP computation in the model corresponding to Equation \eqref{equa7} fitted on the whole dataset \#1. Parameter $\beta_{3}'$ for gymnosperms is grayed since it does not play any role in the model due to the multiplication by $G=0$.}
	\bigskip
	\centering 
	\scriptsize
		\begin{tabular}{lccccccc}
			\hline
			&&&&&& RMSE & RMSE \\
			Genus & $n$ & $\beta_{1}$ & $\beta_{2}+b_{2i}$ & $\beta_{3}'$ & $\beta_{4}+b_{4i}$ & of & of \\
			&&&&&& $VEF$ & $Vtot$ (m$^{3}$) \\
			\hline
			\multicolumn{8}{c}{Angiosperms} \\
			\textit{Betula} & 16 & 6.830 & 1.016 & 1.009 & 0.448 & 0.040 & 0.022 \\	
			\textit{Carpinus} & 77 & 6.830 & 1.133 & 1.009 & 0.822 & 0.146 & 0.099 \\
			\textit{Fagus} & 1987 & 6.830 & 0.842 & 1.009 & 0.627 & 0.200 & 0.200 \\
			\textit{Fraxinus} & 115 & 6.830 & 1.112 & 1.009 & 0.470 & 0.142 & 0.101 \\	
			\textit{Quercus} & 1882 & 6.830 & 1.320 & 1.009 & 0.245 & 0.138 & 0.224 \\
			\hline
			\multicolumn{8}{c}{Gymnosperms} \\
			\textit{Abies} & 1135 & 6.830 & 1.496 & \textcolor{gray}{1.009} & 0.566 & 0.086 & 0.077 \\
			\textit{Larix} & 92 & 6.830 & 0.966 & \textcolor{gray}{1.009} & 0.454 & 0.042 & 0.013 \\
			\textit{Picea} & 330 & 6.830 & 0.953 & \textcolor{gray}{1.009} & 0.473 & 0.039 & 0.048 \\
			\textit{Pinus} & 2168 & 6.830 & 0.566 & \textcolor{gray}{1.009} & 0.336 & 0.096 & 0.042 \\
			\textit{Pseudotsuga} & 390 & 6.830 & 0.744 & \textcolor{gray}{1.009} & 0.783 & 0.088 & 0.023 \\			
			\hline	
		\end{tabular}
	\label{tableMixedModel}
\end{table}

\bigskip
\begin{sidewaystable}[h]
	\caption{Validation of the model on the independent dataset \#2.}
	\bigskip
	\renewcommand{\arraystretch}{0.75}
	\centering 
		\begin{tabular}{llccccc}
			\hline
			&  &  & \multicolumn{2}{c}{Fixed part of the model} & \multicolumn{2}{c}{With species specific coefficients} \\
			Genus & Species & Number of trees & RMSE of the & RMSE of & RMSE of & RMSE of \\
			& & & $VEF$ & $Vtot$ (m$^{3}$) & $VEF$ & $Vtot$ (m$^{3}$) \\
			\hline
			\multicolumn{7}{c}{Tree species used for the model calibration} \\
			\textit{Betula} & \textit{pendula} & 13 & 0.137 & 0.267 & 0.143 & 0.282 \\
			\textit{Carpinus} & \textit{betulus} & 2 & 0.162 & 0.107 & 0.152 & 0.068 \\
			\textit{Fagus} & \textit{sylvatica} & 34 & 0.168 & 0.554 & 0.150 & 0.486 \\			
			\textit{Fraxinus} & \textit{excelsior} & 8 & 0.367 & 1.091 & 0.379 & 1.127 \\
			\textit{Quercus} & \textit{petraea/robur} & 24 & 0.214 & 0.749 & 0.249 & 0.950 \\
			\hline
			\multicolumn{7}{c}{Tree species not used for the model calibration} \\
			\textit{Acer} & \textit{pseudoplatanus} & 23 & 0.130 & 0.099 & - & - \\
			\textit{Alnus} & \textit{sp.} & 16 & 0.159 & 0.215 & - & - \\
			\textit{Pinus} & \textit{halepensis} & 8 & 0.157 & 0.178 & 0.203 & 0.235 \\
			\textit{Populus} & \textit{tremula} & 2 & 0.103 & 0.062 & - & - \\
			\textit{Quercus} & \textit{ilex} & 23 & 1.129 & 0.047 & 0.732 & 0.031 \\
			\textit{Quercus} & \textit{pubescens} & 8 & 0.243 & 0.193 & 0.283 & 0.227 \\
			\textit{Robinia} & \textit{pseudoacacia} & 8 & 0.083 & 0.030 & - & - \\
			\textit{Tilia} & \textit{cordata} & 7 & 0.200 & 0.278 & - & - \\						
			\hline
		\end{tabular}
	\label{RMSE_validation}
\end{sidewaystable}

